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**On boundary conditions for a certain class of problems in mixture theory.**
*(English)*
Zbl 0594.73007

Summary: An additional boundary condition is proposed for solid-fluid mixtures for the situation in which a mixture boundary is in a saturated state. This condition on the boundary is derived from a thermodynamic characterization of the state and takes the form of a relationship between the total stress tensor, the stretch tensor and the volume fraction of the solid. This additional condition is sufficient to make several boundary value problems involving mixtures, determinate.

### MSC:

74A99 | Generalities, axiomatics, foundations of continuum mechanics of solids |

76R99 | Diffusion and convection |

74A20 | Theory of constitutive functions in solid mechanics |

### Keywords:

linearly viscous fluid; nonlinearly elastic solid; Helmholtz free; energy; interacting continua; diffusion; solid-fluid mixtures; mixture boundary; saturated state
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\textit{K. R. Rajagopal} et al., Int. J. Eng. Sci. 24, 1453--1463 (1986; Zbl 0594.73007)

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